For a prime number p, we give a new restriction on pro-p groups G which are realizable as the maximal pro-p Galois group GF(p) for a field F containing a root of unity of order p. This restriction arises from Kummer Theory and the structure of the maximal p-radical extension of F. We study it in the abstract context of pro-p groups G with a continuous homomorphism θ:G→1+pZp, and characterize it cohomologically, and in terms of 1-cocycles on G. This is used to produce new examples of pro-p groups which do not occur as maximal pro-p Galois groups of fields as above

Quadrelli, C., Efrat, I. (2019). The Kummerian Property and Maximal Pro-p Galois Groups. JOURNAL OF ALGEBRA, 525, 284-310 [10.1016/j.jalgebra.2019.01.015].

The Kummerian Property and Maximal Pro-p Galois Groups

Quadrelli, C;
2019

Abstract

For a prime number p, we give a new restriction on pro-p groups G which are realizable as the maximal pro-p Galois group GF(p) for a field F containing a root of unity of order p. This restriction arises from Kummer Theory and the structure of the maximal p-radical extension of F. We study it in the abstract context of pro-p groups G with a continuous homomorphism θ:G→1+pZp, and characterize it cohomologically, and in terms of 1-cocycles on G. This is used to produce new examples of pro-p groups which do not occur as maximal pro-p Galois groups of fields as above
Articolo in rivista - Articolo scientifico
Maximal pro-p Galois groups, Galois cohomology, absolute Galois groups, oriented pro-p groups
English
4-feb-2019
2019
525
284
310
open
Quadrelli, C., Efrat, I. (2019). The Kummerian Property and Maximal Pro-p Galois Groups. JOURNAL OF ALGEBRA, 525, 284-310 [10.1016/j.jalgebra.2019.01.015].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/217752
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